A pre-built computer capable of mining and gaming decently? I'd say that's not possible. You'll get PCs that are able to run most current games at medium settings but it won't be viable for mining.
I used my two years old gaming rig for mining until I realised that after subtracting the electricity cost that PC makes me less money when mining 24/7 than solving some tasks and clicking some ads for an hour or two a day gets me.
Did you have an updated video card?
Nope used the two 5750s that were in it. They aren't the most power effective nor the best cards for mining but are decent for gaming still. Updating the video cards is planned for the release of Star Citizen.
By overclocking I squeezed about 335 MH/s out of them. That would make me about 0.013 BTC per 24 hours on BTCGuild. 90% of that would be used up by the power cost for having the PC running 24 hours. Using task sites I can easily make 0.02 BTC in two hours with no power cost attached to it at all. Hence I decided to stop mining and use the PC for gaming again and earn some BTC by visiting those sites daily.